Integrated readout card

ABSTRACT

An integrated qubit readout circuit is presented, which includes a superconducting parametric amplifier, a circuit board arranged to mount the superconducting parametric amplifier, a circulator mounted on the circuit board and connected to the superconducting parametric amplifier, wherein the circulator comprises a termination port electrically connected to a termination resistor arranged to terminate a pump tone received by the superconducting parametric amplifier, and wherein the termination resistor is mounted on the circuit board.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.62/941,230, filed on Nov. 27, 2019. The disclosure of the priorapplication is considered part of and is incorporated herein byreference in its entirety.

TECHNICAL FIELD

This present disclosure relates to readout systems for qubits.

BACKGROUND

Large-scale quantum computers have the potential to provide fastsolutions to certain classes of difficult problems. Multiple challengesin the design and implementation of quantum architecture to control,program and maintain quantum hardware impede the realization oflarge-scale quantum computing.

SUMMARY

The present disclosure describes technologies for implementing anintegrated readout card for qubits.

In general, one innovative aspect of the subject matter of the presentdisclosure may be embodied in an integrated qubit readout circuitincluding a superconducting parametric amplifier, a circuit boardarranged to mount the superconducting parametric amplifier and acirculator mounted on the circuit board and connected to thesuperconducting parametric amplifier, wherein the circulator comprises atermination port electrically connected to a termination resistorarranged to terminate a pump tone received by the superconductingparametric amplifier, and wherein the termination resistor is mounted onthe circuit board.

The foregoing and other implementations can each optionally include oneor more of the following features, alone or in combination.

In some implementations, at least part of an external surface of thetermination resistor is in direct contact with the circuit board.

In some implementations, at least part of an external surface of thecirculator is in direct contact with the circuit board.

In some implementations, the circuit board comprises a front planelayer, a signal layer, a back plane layer, and a support layer. Thefront plane layer is disposed on a first side of the support layer andthe back plane layer is disposed on a second side of the support layerthat is opposite to the first side. The signal layer is disposed betweenthe front plane layer and the back plane layer within the support layer.The circulator and the termination resistor are mounted on the firstside of the support layer such that at least one surface of thecirculator and the termination resistor is in direct contact with thefront plane layer.

In some implementations, the superconducting parametric amplifier ismounted on the signal layer.

In some implementations, the front plane layer, the second signal layerand the back plane layer comprise a second conductor whose thermalconductivity is larger than 300 W/m/K at 10 mK temperature, and thecirculator and the termination resistor are mounted on the front planelayer.

In some implementations, the support layer comprises a first viaarranged to electrically and thermally connect a first part of the frontplane layer in contact with the at least part of an external surface ofthe circulator to the back plane layer, and the support layer comprisesa second via arranged to electrically connect a second part of the frontplane layer to the signal layer.

In some implementations, the first conductor comprises aluminum and thesecond conductor comprises copper.

In some implementations, the back plane layer is connectable to a heatsink.

In some implementations, the at least part of the external surface ofthe circulator in direct contact with the circuit board comprises amaterial whose thermal conductivity is larger than 300 W/m/K at 10 mKtemperature.

In some implementations, the integrated qubit readout circuit furthercomprises a magnetic shield disposed around the superconductingparametric amplifier, arranged to shield the superconducting parametricamplifier from magnetic fields of the circulator.

In some implementations, the magnetic shield comprises a tube-shapedbody comprising a mu-metal arranged to enclose the superconductingparametric amplifier when the magnetic shield is mounted on the circuitboard.

In some implementations, the circuit board comprises a first slotarranged on a first side of the superconducting parametric amplifier anda second slot arranged on a second side of the superconductingparametric amplifier. The first slot and the second slot are dimensionedso as to receive the magnetic shield, and a distance between the firstslot and the second slot matches a diameter of the magnetic shield.

In some implementations, the first signal layer comprises a strip linewaveguide.

In some implementations, the first signal layer comprises a directionalcoupler formed with the strip line waveguide.

In some implementations, the circulator comprises a passive ferritecirculator.

In some implementations, the termination resistor comprises a 50 Ohmresistor.

In some implementations, a qubit readout assembly is provided whichincludes an expansion board connectable to a cold finger of a cryostat,a plurality of the integrated qubit readout circuits. The expansionboard is configured to receive the plurality of the integrated qubitreadout circuits such that the plurality of the integrated qubit readoutcircuits are mounted on the expansion board. The expansion board isconfigured such that the expansion board and the plurality of theintegrated qubit readout circuits are in a thermal equilibrium with thecold finger of the cryostat when the expansion board is connected to thecold finger and the plurality of the integrated qubit readout circuitsare mounted on the expansion board. The expansion board is configured toprovide electrical connections between a circuit in contact with thecold finger and the plurality of the integrated qubit readout circuits.

The details of embodiments are set forth in the accompanying drawingsand the description below. Other aspects will be apparent from thedescription and drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic that illustrates an exemplary qubit readoutcircuit.

FIGS. 2a to 2c are schematics that illustrate an exemplary integratedcircuit board for qubit readout circuit

FIGS. 3a to 3c are schematics that illustrate aspects of an exemplaryqubit readout circuit implemented on an integrated circuit board.

FIG. 4 is a schematic that illustrates an exemplary qubit readoutassembly.

DETAILED DESCRIPTION

Quantum computing entails coherently processing quantum informationstored in the quantum bits (qubits) of a quantum computer.Superconducting quantum computing is a promising implementation ofsolid-state quantum computing technology in which quantum informationprocessing systems are formed, in part, from superconducting materials.To operate quantum information processing systems that employsolid-state quantum computing technology, such as superconductingqubits, the systems are maintained at extremely low temperatures, e.g.,in the 10 s of mK. The extreme cooling of the systems keepssuperconducting materials below their critical temperature and helpsavoid unwanted state transitions. To maintain such low temperatures, thequantum information processing systems may be operated within acryostat, such as a dilution refrigerator.

In some implementations, control signals are generated inhigher-temperature environments, such as room-temperature, and aretransmitted to the quantum information processing system using shieldedimpedance-controlled GHz-capable transmission lines, such as coaxialcables. The cryostat may step down from room-temperature (e.g., about300 K) to the operating temperature of the qubits in one or moreintermediate cooling stages. For instance, the cryostat may employ astage maintained at a temperature range that is colder than roomtemperature stage by one or two orders of magnitude, e.g., about 30-40 Kor about 3-4 K, and warmer than the operating temperature for the qubits(e.g., about 10 mK or less).

In some implementations, the state measurement of superconducting qubitsis achieved using a dispersive detection scheme. In order to read out ordetect the state of any qubit, a probing signal, a travelling microwave,may be excited along a readout transmission line coupled to the qubitvia a respective readout resonator. The frequency of the probing signalmay be in the vicinity of the resonance frequency of the readoutresonator. Depending on the internal quantum mechanical state of thequbit, the intensity and the phase of the probing signal transmittedalong the readout transmission line may be altered because thereflectivity of the readout resonator coupled to the qubit changesdepending on the state of the qubit. This allows for the state detectionof the qubits.

Even at the extremely low qubit operating temperatures, qubits may stillsuffer from decoherence and gate errors. Therefore, for high fidelitystate measurements of superconducting qubits with near quantum-limitednoise performance, a Josephson junction parametric amplifier may beconstructed and used as a preamplifier for the probing signal. Withinthe Josephson junction parametric amplifier, a Josephson junction actsas a nonlinear inductor where the inductance is dependent on theintensity of a pump tone received at the Josephson junction. In otherwords, the inductance of the Josephson junction is dependent on the fluxapplied through a SQUID loop which includes the Josephson junction. Thisinductance can be modulated by applying a flux pump tone to the SQUIDloop. The Josephson junction parametric amplifier can impart part of theenergy of the pump tone to the probing signal, leading to the parametricamplification of the probing signal.

The dispersive detection scheme further requires, in addition to theJosephson junction parametric amplifier as a preamplifier, circulatorsfor isolation of the signals and directional couplers for combiningsignals. In particular, using circulators for isolation requiresimpedance matching with a terminating resistor attached one of the portsof the circulators for termination, as will be explained later. Due tothe heat dissipated, it is crucial to properly thermalize thetermination resistor, such as a 50 Ohm resistor within the cryostat. Asthe number of qubits increases, the number of the termination resistorsattached to the circulators also increases, which may raise a challengein thermalizing all of the termination resistors properly inside acryostat. If the termination resistors are not well thermalized, thetemperature of the termination resistors may stay higher than that ofthe base temperature of the cryostat. The energy dissipated at the 50Ohm resistors may radiate noise which can affect qubit performance andlead to degradation of the coherence via dephasing of the qubits.

Using conventional prototype hardware for circulators, directionalcouplers, and termination resistors for the dispersive readout schememay not be suitable for superconducting quantum systems with a largenumber of qubits to implement error correction algorithms. This ismainly due to the constraint in the available space within the cryostat.Since all of the hardware for the dispersive readout scheme must bemounted on a mix plate at the mK-stage of the dilution refrigerator,space constraints become severe as the number of qubits increases. Thenumber of modules which can fit in the available volume within thedilution refrigerator may be limited if the modules are assembled usingconventional prototype hardware. A typical number of readout lines insuch a system is 12. Additionally, the conventional prototype hardwaredoes not lend itself easily to efficient thermalization. For example, incase the 50 Ohm resistor is provided by a 50 Ohm SubMiniature version A(SMA) terminator cap, the heat generated at the 50 Ohm SMA terminatorcap may be difficult to thermalize properly because of the geometry ofthe SMA terminator which does not allow a large surface contact forcooling. Furthermore, using multiple SMA connectors in the signal pathmay lead to signal loss which lowers the signal to noise ratio of thedetected signals.

The present disclosure relates to an integrated circuit board on whichcomponents of the dispersive readout scheme are mounted together. Theintegrated circuit board may also be referred to as an “integratedreadout card”. The integrated circuit board may include the Josephsonjunction preamplifiers, circulators and 50 Ohm terminators directlymounted on the circuit board. These components can be connected bysignal lines fabricated directly on a conducting layer on the integratedcircuit board for low loss connection between components and reducedvolume. Directional couplers can be directly fabricated on theconducting layer out of the signal lines to further reduce the volume ofthe readout circuit. This allows for a compact design in which mostcomponents can be surface mounted and soldered or wire bonded directlyinto the circuit board.

The integrated circuit board may contain multiple conducting layers. Asignal layer may be buried within the volume of a dielectric supportlayer. A front plane layer and a back plane layer may be provided onboth sides of the support layer to serve as an electric ground and athermal anchor. Most of the components can be mounted on the front planelayer to have a large surface contact with the front plane layer. Sincethe front plane layer and the back plane layer are connected withconducting vias, heat generated from the components may be dissipatedefficiently to the back plane layer, which is again connected to a heatsink or directly to the mixing plate of the dilution refrigerator. Suchintegrated circuit board may allow for a high degree of integration ofthe readout circuit compact while providing an efficient thermalization.

FIG. 1 is a schematic that illustrates an exemplary qubit readoutcircuit.

A qubit readout circuit 100 may include a first circulator 111, a secondcirculator 112, a third circulator 113 and a fourth circulator 114. Thequbit readout circuit 100 further includes a first termination resistor121, a second termination resistor 122, a third termination resistor 123and a fourth termination resistor 124. The qubit readout circuit 100further includes a Josephson parametric amplifier 130.

A circulator 110 is a passive device which usually includes three orfour ports. A signal entering one of the ports 110-1, 110-2, 110-3 istransmitted to another one of the ports 110-1, 110-2, 110-3 but only inone direction. As illustrated on the right panel of FIG. 1, a circulator110 in this implementation includes three ports 110-1, 110-2, 110-3. Asillustrated with dotted lines in the right panel, when a signal entersthe first port 110-1 of the isolator 110, the signal is transmitted tothe second port 110-2 of the circulator 110 and exits the second port110-2 of the circulator 110. When a signal enters the second port 110-2of the circulator 110, the signal is transmitted to the third port110-3, but not the first port 110-1, and exits at the third port 110-3of the circulator 110. Throughout this implementation, a first port, asecond port, and a third port included in the first to fourthcirculators 111, 112, 113, 114 follow this convention.

In the readout circuit 100, an input signal is received at the firstport 111-1 of the first circulator 111.

In some implementations, the input signal may be provided by atravelling microwave reflected from a readout resonator coupled to aqubit. The frequency of the travelling microwave, a probe signal, may beat the resonance frequency or in the vicinity of the resonance frequencyof the readout resonator. Since the readout resonator is coupled to thequbit, the resonance frequency of the readout resonator changesdepending on the state of the qubit. Therefore, depending on theinternal quantum mechanical state of the qubit, the intensity or phaseof the probing signal may be altered, which allows for the statedetection of the qubits.

In some implementations, the input signal may be provided by atravelling microwave reflected from one of a plurality of readoutresonators coupled to a plurality of respective qubits. The plurality ofreadout resonators may be coupled to a common readout transmission line.A travelling microwave, a probe signal, may be excited to travel alongthe readout transmission line. The frequency of the probe signal, may beat the resonance frequency or in the vicinity of the resonance frequencyof one of the readout resonators. Since the plurality of readoutresonators are coupled to the plurality of respective qubits, theresonance frequency of the readout resonator changes depending on thestate of the qubit. Therefore, depending on the internal quantummechanical state of the probed qubit, the intensity or phase of theprobing signal may be altered, which allows for the state detection ofthe qubits.

In some implementations, the input signal may be provided by a probesignal comprising multiple tones of a travelling microwave reflectedfrom a respective plurality of readout resonators coupled to a pluralityof respective qubits. The plurality of readout resonators may be coupledto a common readout transmission line. The frequency of each of themultiple tones of the probe signal, may be at the resonance frequency orin the vicinity of the resonance frequency of a respective one or theplurality of the readout resonators. Since the plurality of readoutresonators are coupled to the plurality of respective qubits, theresonance frequency of the readout resonator changes depending on thestate of the qubit. Therefore, depending on the internal quantummechanical state of the probed qubits, the intensity or phase of eachtone of the probing signal may be altered, which allows for the statedetection of the qubits.

In the example of FIG. 1, a reflection scheme for measuring the statesof the qubits is shown where only one line connects the qubit chip tothe readout circuit 100 via a directional coupler 10. The probing signalis input into an input port 10-1 of the directional coupler 10. Most ofthe power of the probing signal input into the input port 10-1 isdissipated at the third termination resistor 123. A fraction of power,determined by the coupling coefficient of the directional coupler 10, ofthe probing signal is coupled into a coupled port 10-2 of thedirectional coupler 10 and sent to the plurality of readout resonatorsrespectively coupled to the plurality of qubits in the qubit chip.Therefore, the intensity or power of the probing signal input into theinput port 10-1 of the directional coupler 10 is set to be larger thanthe level of intensity or power intended for the readout circuit 100 inview of the coupling coefficient of the directional coupler 10. Thecoupling coefficient of the directional coupler 10 may be decided byconsidering parameters including the signal-to-noise ratio of themeasurement and heat dissipation at the third termination resistor 123.The coupling coefficient of the directional coupler 10 may be set to beas low as possible in order to minimize the attenuation of the probingsignal reflected off the readout resonators at the directional coupler10 before the probing signal is input into the first port 111-1 of thefirst circulator 111. However, this is balanced by the fact that thepower of the probing signal 10-1 needs to be accordingly large tomaintain the level of the probing signal in the readout circuit 100,which increases heat dissipation at the third termination resistor 123.

The probe signal is then transmitted to the second port 111-2 of thefirst circulator 111 and exits the first circulator 111 through thesecond port 111-2 and passes to the second circulator 112. The thirdport 111-3 of the first circulator 111 is terminated with the firsttermination resistor 121. The first to fourth termination resistors 121,122, 123, 124 are a matched load to the transmission line forming thecirculators 111, 112, 113, 114 and the connections between thecirculators 111, 112, 113, 114. For example, when the impedance of thetransmission lines is 50 Ohms, the resistance of the terminationresistors 121, 122, 123, 124 is 50 Ohms.

If any signal is transmitted back to the second port 111-2 of the firstcirculator 111 reflected from a component in the later stage of thequbit readout circuit 100, the reflected signal exits from the thirdport 111-3 of the first circulator 111 and becomes terminated ordissipated at the first termination resistor 121. Therefore, between theunterminated ports of the first circulator 111, the first port 111-1 andthe second port 111-2 of the first circulator 111, the signal can travelonly in one direction, namely from the first port 111-1 to the secondport 111-2. Therefore, a circulator 111, 112, 113, 114 with the thirdport 110-3, 111-3, 112-3, 113-3, 114-3 terminated with a terminationresistor 121, 122, 123 acts as an isolator, which is used to shieldcomponents coupled to the first port 110-1, 111-1, 112-1, 113-1, 114-1from any back-propagating microwave signals from the subsequentcomponents.

In the qubit readout circuit 100, the third ports 111-3, 112-3, 114-3 ofthe first circulator 111, the second circulator 112, and the fourthcirculator 114 are terminated with the first termination resistor 121,the second termination resistor 122, and the fourth termination resistor124, respectively, therefore configured as isolators. These are toprotect the qubits connected to the first port 111-1 of the firstcirculator 111 from back-propagating signals, as will be explained inmore detail below.

The second port 111-2 of the first circulator 111 is electricallyconnected, via a matched transmission line, to the first port 112-1 ofthe second circulator 112. The third port 112-3 of the second circulator112 is terminated with the second termination resistor 122. Therefore,as discussed above, the second circulator 112 also forms an isolatorfrom the first port 112-1 to the second port 112-2. When the probesignal outputted from the second port 111-2 of the first circulator 111enters the first port 112-1 of the second circulator 112, the probesignal exits the second port 112-2. If any back-reflected spurioussignal enters the second port 112-2 of the second circulator 112, it issubsequently transmitted to the third port 112-3 of the secondcirculator 112 and terminated. Therefore, the second circulator 112 isterminated with the second termination resistor 122 at the third port112-3 which serves as a further shielding of the qubits in addition tothe isolator formed by the first circulator 111 and the firsttermination resistor 121.

The second port 112-2 of the second circulator 112 is electricallyconnected, via a matched transmission line, to the first port 113-1 ofthe third circulator 113. The probe signal enters the first port 113-1of the third circulator 113 and exits through the second port 113-2 ofthe third circulator towards the Josephson junction parametric amplifier130.

Parametric amplifiers are nonlinear devices in which a reactance in thecircuit is modulated by a pump tone of frequency fp to facilitateamplification and frequency conversion from a first band of frequenciesΔf centered around f1 to a second band of frequencies Δf centered aroundf2, such that fp=f1+f2.

For example, if a pump tone at 11 GHz is provided to the Josephsonjunction parametric amplifier 130 and the frequency of the probe signalis 5 GHz, the Josephson junction parametric amplifier 130 up-convertsthe frequency of the first signal into 6 GHz. If a pump tone at 10 GHzis provided to the Josephson junction parametric amplifier 130 and thefrequency of the probe signal is 5 GHz, the Josephson junctionparametric amplifier 130 outputs a signal at 5 GHz. In both cases, theintensity of the probe signal can be amplified to a degree dependent onthe amplitude of the pump tone. In both cases, the probe signal at 5 GHzis also amplified.

The pump tone is received at the Josephson parametric amplifier 130 viaa pump terminal 131.

The Josephson junction parametric amplifier 130 outputs an amplifiedprobe signal back into the second port 113-2 of the third circulator113. The amplified probe signal exits through the third port 113-3 ofthe third circulator 113.

In some implementations, in place of the Josephson junction parametricamplifier 130, the Josephson junction parametric converter may be usedfor the qubit readout circuit 100. Parametric converters are nonlineardevices in which a reactance in the circuit is modulated by a pump toneof frequency fp to facilitate amplification and frequency conversionfrom a first band of frequencies Δf centered around f1 to a second bandof frequencies Δf centered around f2, such that fp=f2−f1.

The amplified probe signal enters the first port 114-1 of the fourthcirculator 114 and is outputted at the second port 114-2 of the fourthcirculator 114. Since the third port 114-3 of the fourth circulator 114is terminated with the fourth termination resistor 124, the fourthcirculator also acts as an isolator.

In some implementations, the qubit readout circuit 100 may correspond toa pre-amplification stage before the signals are combined or multiplexedfor further amplification. For example, the output signal from thesecond port 114-2 of the fourth circulator 114 may be amplified by aHEMT (High Electron Mobility Transistor) amplifier before processing.

The number of isolators, which are circulators 111, 112, 114 terminatedwith a termination resistors 121, 122, 124, required for the qubitreadout circuit 100 may vary depending on the requirement or thecomponents attached to the output of the qubit readout circuit 100.

The qubit readout circuit 100 shown in FIG. 1 includes one isolator 114,124 between the output terminal 114-2 and the Josephson junctionparametric amplifier 130. This is mainly to shield the Josephsonjunction parametric amplifier from the signals reflected from subsequentcomponents, such as a HEMT amplifier. The degree of isolation may dependon the isolation ratio of each circulator 111, 112, 114, which rangesfrom 20 to 40 dB rejection. If a higher degree of isolation is required,further isolators, which are circulators terminated with a terminationresistor, can be cascaded to the second port 114-2 of the fourthcirculator 114.

The qubit readout circuit 100 shown in FIG. 1 includes two isolators111, 112, 121, 122 between the input terminal 111-1 and the Josephsonjunction parametric amplifier 130. This is mainly to shield the qubitsfrom either the pump tone propagating from the Josephson parametricamplifier 130 or amplified noise emitted from the Josephson parametricamplifier 130. Since the circulator 111, 112, 113, 114 have a finitebandwidth, the pump tone may be out of band with the circulators 111,112, 113, 114. For example, when the circulator operates from 4 to 7 GHzand the frequencies of the probe signal and the amplified probe signalare at 5 GHz, the frequency of the pump tone is 10 GHz, which is out ofband of the operation bandwidth of the circulator. Therefore, theisolation ratio of the circulators 111, 112 may be lower than specified.Also, when the pump tone is far away from the resonance frequencies ofthe readout resonators in the qubit chip, it may not affect theperformance of the qubits significantly. Therefore, the two isolators111, 112, 121, 122 between the input terminal 111-1 and the Josephsonjunction parametric amplifier 130 may be mainly used to suppress theamplified noise from the Josephson junction parametric amplifier frompropagating to the qubits. The pump tone whose intensity is 10's of nW,is in general much more intense than the probe signal. For example, thepower of the pump tone may be from −70 dBm to −40 dBm whereas the powerof the probe signal may be from −130 to −110 dBm. If a higher degree ofisolation is required, further isolators, each comprising a circulatorterminated with a termination resistor, can be disposed between theinput port 111-1 and the first port 113-1 of the third circulator 113.Therefore, if the readout circuit 100 may be designed such that moreisolators can be added without occupying much volume within theexperimental space of the cryostat.

Any unwanted signals propagating the wrong direction through acirculator 111, 112, 113, 114 will be terminated at the terminationresistors 121, 122, 123, 124. Properly thermalizing the terminatingresistors 121, 122, 123, 124 may prevent this energy from re-radiatingtoward the qubit, which can otherwise affect the coherence of thequbits. In addition to the termination resistors, 121, 122, 123, 124,which are the major sources of heat dissipation, the circulators 111,112, 113, 114 themselves may dissipate heat because the conductorswithin the circulators 111, 112, 113, 114 which have finite resistancecan dissipate the pump tone. Therefore, the heat dissipated at the qubitreadout circuit 100 needs to be efficiently channeled to a heat sink forthe coherence of the qubits.

FIGS. 2a to 2c are schematics that illustrate an exemplary integratedcircuit board for a qubit readout circuit shown in FIG. 1.

FIGS. 2a and 2b show a circulator 210, which can be any one of thecirculators 111, 112, 113, 114 shown in FIG. 1, mounted on an integratedcircuit board 200. FIGS. 2a and 2b show the circulator 210 mounted onthe integrated circuit board 200 viewed in two different directions. Inparticular, FIG. 2a shows a cross section of the integrated circuitboard 200 and the circulator 210, along the y-z plane and FIG. 2b showsa cross section of the integrated circuit board 200 and the circulator210, along the x-z plane.

As shown in FIG. 2a , the circulator 210 includes a first port 210-1 anda second port 210-2. As shown in FIG. 2b , the circulator 210 furtherincludes a third port 210-3 which is electrically connected to atermination resistor 220.

The integrated circuit board 200 includes three conducting layers, afront plane layer 230, a signal layer 240 and a back plane layer 250 andone dielectric layer, a first support layer 260-1 and a second supportlayer 260-2. The first support layer 260-1 is disposed between the frontplane layer 230 and the signal layer 240. The second support layer 260-2is disposed between the signal layer 240 and the back plane layer 250.

In some implementations, the front plane layer 230, the signal layer 240and the back plane layer 250 are substantially parallel to one another.

In some implementations, the front plane layer 230, the signal layer 240and the back plane layer 250 comprise the same conducting material.

In some implementations, the front plane layer 230, the signal layer 240and the back plane layer 250 comprise copper which provides a highthermal conductivity for efficient thermalization and a high electricalconductivity such that a significant signal loss is prevented within theintegrated circuit board 200. It is not essential for the front planelayer 230, the signal layer 240 or the back plane layer 250 to besuperconducting at the operating temperature of the qubits.

In some implementations, the back plane layer 250 may comprise aluminum.Aluminum is superconducting at the temperature given by the mixing plateof the dilution refrigerator. Therefore, the signal transmission becomeslargely lossless.

The Josephson junction parametric amplifier 130 may be formed on aseparate chip comprising an aluminum layer and electrically connected tothe signal layer 240 via, for example, wire bonding.

The first support layer 260-1 and the second support layer 260-2 providean overall planar shape of the integrated circuit board.

The examples of the material for the first support layer 260-1 and thesecond support layer 260-2 include a dielectric material such as Rogers,which is both compatible with microwave circuits and cryogenictemperatures.

In some implementations, the front plane layer 230 and the back planelayer 250 may be disposed on both sides of the plane of the supportlayer 260, as shown in FIGS. 2a and 2 b.

In some implementations, the signal layer 240 is buried within thesupport layer 260 and not exposed to the outside environment.

In some implementations, the signal layer 240 may comprise one or morestripline waveguides, where the waveguide circuit is defined by stripsof metal fabricated within the signal layer 240, and the front planelayer 230 and the back plane layer 250 act as ground planes.

In some implementations, the front plane layer 230 may comprise one ormore co-planar waveguides, where the waveguide circuit is defined by thestrips of metal fabricated within the front plane layer 230 with returntracks defined on either side of the strips, also fabricated within thefront plane layer 230.

The stripline waveguides comprised by the signal layer 240 may form awaveguide circuit within in a plane parallel to the front plane layer230 and the back plane layer 250.

In some implementations, in case the signal layer 240 is buried withinthe support layers 260-1, 260-2, the plane within which the signal layer240 is formed may be equidistant from the front plane layer 230 and theback plane layer 250. For example, if the signal layer 240 comprises oneor more stripline waveguides, in order to ensure 50 Ohm impedance in thestripline waveguides throughout the plane of the signal layer, thesignal layer 240 is positioned equidistant from the plane layer 230 andthe back plane layer 250. However, as far as the signal layer 240 is notexposed from the support layer 260, and the waveguides comprised by thesignal layer 240 can maintain the impedance required for the operation,the position of the signal layer 240 can be anywhere between the frontplane layer 230 and the back plane layer 250.

In some implementations, the front plane layer 230 may be patterned toform one or more solder pads 231. The solder pads 231 can be patternedsuch that they are electrically disconnected from an electric groundformed in other regions of the front plane layer 230, which will form anelectric ground.

In some implementations, as shown in FIGS. 2a and 2b , the terminals ofthe circulator 210, forming respectively the first port 210-1, thesecond port 210-2, and the third port 210-3 of the circulator 210, aredirectly wire bonded to the solder pads 231.

Alternatively, the terminals of the circulator 210, forming respectivelythe first port 210-1, the second port 210-2, and the third port 210-3 ofthe circulator 210, may include conducting pins. In this case, theconducting pins can be directly soldered to the solder pads 231.

The area of the solder pads 231 are arranged to be large enough for wirebonding or soldering to be possible.

The electrical connection between the ports 210-1, 210-2, 210-3 of thecirculator 210 and the solder pads 231 are not limited to wire bondingor soldering. As long as the connection is compatible with highfrequency signals, for example 1 MHz or higher, and the connection canwithstand a cryogenic temperature of operation, any connection methodcan be used.

The integrated circuit board 200 further includes one or more signalvias 241. The signal vias 241 comprise a conducting material. In someimplementations, the signal vias 241 comprise the same material as thefront plane layer 230 and the signal layer 240. In some implementations,the signal vias extend in a direction perpendicular to the plane of theintegrated circuit board 200 and electrically connects the solder pads231 to the respective signal lines within the signal layer 240. In someimplementations, the signal vias 241 extend in any direction from thefront plane layer 230 to the signal layer 240 to electrically connectthe solder pads 231 to the respective signal lines within the signallayer 240.

In the cross sections shown in the example of FIGS. 2a and 2b , only thesignal lines connected to the solder pads 231 connected to the firstport 210-1 and the second port 210-2 are shown. Therefore, the crosssection of the integrated circuit board 200 shown in FIG. 2b does notshow any part of the signal line 240.

Parts of the front plane layer 230 which are not connected to the solderpads 231 form an electrical ground.

The integrated circuit board 200 further includes one or more groundvias 251. The ground vias 251 comprise a conducting material. In someimplementations, the ground vias 251 comprise the same material as thefront plane layer 230 and the back plane layer 250. In someimplementations, the ground vias 251 extend in a direction perpendicularto the plane of the integrated circuit board 200 and electricallyconnects part of the front plane layer 230 not electrically connected tothe solder pads 231 to the back plane layer 250. In someimplementations, the ground vias 251 extend in any direction from thefront plane layer 230 to the back plane layer 250 to electricallyconnect part of the front plane layer 230 not electrically connected tothe solder pads 231 to the back plane layer 250.

The part of the front plane layer 230 not electrically connected to thesolder pads 231 and the back plane layer 250, connected to each othervia the ground vias 251 form an electrical ground.

Heat dissipated into the front plane layer 230 is transferred to theback plane layer 250 via the ground vias 251. Therefore, the crosssection of the ground vias 251 may be arranged such that the ground vias251 can transmit heat from the front plane layer to the back plane layerwithout heating up significantly at any point of the ground vias 251.

In some implementations, the back plane layer 230 may be arranged to bein direct contact with the mixing plate of the dilution refrigeratorsuch that heat transferred to the back plane layer 230 is taken from theintegrated circuit board 200 and dissipated.

Alternatively, the back plane layer 230 is arranged to be in a shapeconnectable to a heat sink, which can be maintained at a thermalequilibrium with the mixing plate of the dilution refrigerator.

FIGS. 2a and 2b show that the circulator 210 and the terminationresistor 220 are surface mounted on the front plane layer 230. In someimplementations, the circulator 210 and the termination resistor 220 maybe constructed as a so-called “drop-in” component, which has alow-profile shape such that the surface contact area with the frontplane layer 230 can be made as large as possible for efficientthermalization.

In some implementations, one or more sunken holes are formed within thesupport layer 260 to house the circulator 210 or the terminationresistor 220.

The external surface of the circulator 210 is made of steel to form thefield lines within the circulator 210 as desired for operation. In someimplementations, the material of the external surface of the circulator210 may further comprise annealed copper layer for thermalizing.

FIG. 2b shows that the termination resistor 220 is mounted on the frontplane layer 230. FIG. 2b further shows that one end of the terminationresistor 220 is electrically connected to the third terminal 210-3 ofthe circulator 210 via one of the solder pads 231 and that the other endof the termination resistor 220 is connected to the part of the frontplane layer 230 which serves as an electric ground.

In some implementations, the external surface of the terminationresistor 220, except the part which makes electrical connections withthe solder pad 231 and the front plane layer 230, may be formed with amaterial which is not electrically conducting but has a high thermalconductivity at a cryogenic temperature.

FIG. 2c shows a top view of the integrated circuit board 200 and thefirst circulator 111, 211, the second circulator 112, 212, the fourthcirculator 114, 214 from the qubit readout circuit 100 of FIG. 1,mounted on the front plane layer 230. As discussed above in FIG. 1, thethird ports 111-3, 211-3, 112-3, 212-3, 114-3, 214-3 of the firstcirculator 111, 211, the second circulator 112, 212, the fourthcirculator 114, 214 are each connected to a termination resistor 121,221, 122, 222, 124, 224 such that the first circulator 111, 211, thesecond circulator 112, 212, the fourth circulator 114, 214 eachfunctions as an isolator.

The front plane layer 230 is patterned such that the support layer 260is exposed around the periphery of the circulators 211, 212, 214,represented in FIG. 2c as unshaded areas. Although not shown beingblocked by the circulators 211, 212, 214, underneath each circulator211, 212, 214, part of the front plane layer 230 is patterned to be incontact with the surface of the circulators 211, 212, 214. As shown inFIGS. 2a and 2b , these hidden parts of the front plane layer 230 areconnected to the back plane layer 250 via the ground vias 251 forefficient thermal transfer.

FIG. 2c shows that the first ports 211-1, 212-1, 214-1 and the secondports 211-2, 212-2, 214-2 of the circulators 211, 212, 214 areelectrically connected to respective solder pads 231. As discussedabove, these electrical connections can be achieved either via directsoldering or wire bonding.

FIG. 2c shows that the third ports 211-3, 212-3, 214-3 of thecirculators 211, 212, 214 are electrically connected to one end of thefirst termination resistor 221, the second termination resistor 222 andthe fourth termination resistor 224, respectively. These connections aremade directly without solder pads 231, for example, either via directsoldering or wire bonding. The other end of the first terminationresistor 221, the second termination resistor 222 and the fourthtermination resistor 224 is electrically connected to the front planelayer 230.

Although not shown blocked by the first termination resistor 221, thesecond termination resistor 222 and the fourth termination resistor 224,part of the front plane layer 230 are in contact with the bottomsurfaces of the first termination resistor 221, the second terminationresistor 222 and the fourth termination resistor 224 for thermalcontact. These parts of the front plane layer 230 in contact with thebottom surfaces of the termination resistors 221, 222, 224 areintegrally formed with the part of the front plane layer 230 which formsan electric ground and connected to the back plane layer 250 vias groundvias 251.

Compared to the case where connectors are used for electricalconnections, such as stainless steel SMA connector, the integratedcircuit board 200 may allow for more compact implementation andtransmission of the signals with less loss. In case the front planelayer 230, the signal layer 240, the back plane layer 250, the signalvias 241, the ground vias 251 comprise a metal with high thermalconductivity, such as copper, direct contact of the components with thecopper allows for more efficient thermalization.

FIG. 3a is a schematic that illustrates an exemplary integrated circuitboard for a qubit readout circuit with references to FIGS. 1 and 2. Inparticular, FIG. 3a shows a CAD drawing of a top view plan of theintegrated circuit board 300 described in FIG. 2 to implement the qubitreadout circuit 100 described in FIG. 1.

The integrated circuit board 300 includes four sites for the circulators111, 211, 112, 212, 113, 114, 214, namely a first site 311 for the firstcirculator 111, 211, a second site 312 for the second circulator 112,212, a third site 313 for the third circulator 113, and a fourth site314 for the fourth circulator 114, 214.

The integrated circuit board 300 further includes a site for theJosephson junction parametric amplifier 370. The Josephson junctionparametric amplifier 370 is implemented on a separate chip from theintegrated circuit board 300, and can be wire bonded to the integratedcircuit board 300.

The integrated circuit board 300 further includes an input terminal301-1, an excite terminal 301-2, an output terminal 302, a pump terminal303. Referring to FIG. 1, the input terminal 301-1 is the coupled port10-2 of the directional coupler 10 and the excite terminal 301-2 is theinput port 10-1 of the directional coupler 10. As explained in FIG. 1,the probe signal is input into the excite terminal 301-2. A portion ofthe probe signal is coupled into input terminal 301-1 and sent to theplurality of readout resonators coupled respectively to the plurality ofqubits. The probe signal reflected from the plurality of readoutresonators are transmitted back to the input terminal 301-1 and entersthe integrated circuit board 300.

Each site 311, 312, 313, 314 includes three solder pad areas 331. Thesolder pad areas 331 are labelled in FIG. 3a as 1, 2, 3 corresponding torespectively the first ports 111-1, 211-1, 112-1, 212-1, 113-1, 114-1,214-1, the second ports 111-2, 211-2, 112-2, 212-2, 113-2, 114-2, 214-2and the third ports 111-3, 211-3, 112-3, 212-3, 113-3, 114-3, 214-3 ofthe circulators 111, 211, 112, 212, 113, 114, 214.

FIG. 3a shows that the solder pad areas 331 of the sites 311, 312, 313,314 are connected as described in FIG. 1. For example, the solder padarea 331 of the first site 311 which is labelled as ‘1’ is connected tothe input terminal 301. The solder pad area 331 of the fourth site 314which is labelled as ‘2’ is connected to an output terminal 302. Thepump port 303 is connected to the site for the Josephson junctionparametric amplifier 370.

As discussed above in FIG. 2, each of the sites 311, 312, 313, 314 arearranged such that when the circulators 111, 211, 112, 212, 113, 114,214 are mounted, at least part of the front plane layer 230 are incontact with at least one of the external surface of the circulators111, 211, 112, 212, 113, 114, 214 for thermalization. The part of thefront plane layer 230 which is to come in contact with the circulators111, 211, 112, 212, 113, 114, 214 when the circulators 111, 211, 112,212, 113, 114, 214 are mounted, are electrically and thermally connectedto the back plane layer 250 via ground vias 251.

In some implementations, the sites 311, 312, 313, 314 may be formed bypatterning the front plane layer 250, as depicted in FIGS. 2a and 2bsuch that at least one surface of the circulators 110, 210, 111, 211,112, 212, 113, 114, 214 and the termination resistor 120, 220, 121, 221,122, 222, 123, 124, 224 are in contact with the front plane layer 230.

In some implementations, the front plane layer 230 may be configured tohave a sunken hole which houses the circulators 110, 210, 111, 211, 112,212, 113, 114, 214 or the termination resistors 120, 220, 121, 221, 122,222, 123, 124, 224. In this case, the front plane layer 230 and thesignal layer 240 may be rearranged accordingly to facilitate electricalconnections and efficient thermalization.

For example, in some implementations, the first support layer 260-1 maybe formed to have a sunken hole such that the part of the front planelayer 230 to be in contact with one of the external surfaces of thecirculators 110, 210, 111, 211, 112, 212, 113, 114, 214 forthermalization. This is to align the front plane layer 240 with theelectrical connections or the ports 210-1, 210-2, 210-3, 210-1, 211-2,211-3, 212-1, 212-2, 212-3, 213-1, 213-2, 213-3 of the circulators 210,211, 212, 213 which may be positioned higher than the bottom surfaces ofthe circulators 210, 211, 212, 213.

Since the electrical terminals of the circulators 110, 210, 111, 211,112, 212, 113, 114, 214 or the termination resistors 120, 220, 121, 221,122, 222, 123, 124, 224 may be formed on the side surfaces, along thex-z plane or the y-z plane in FIG. 2, the distance between the planewith the solder pads 231 and the lowered front plane 230, or the bottomof the sunken hole, or the plane in contact with the external surfacesof the circulators 110, 210, 111, 211, 112, 212, 113, 114, 214 or thetermination resistors 120, 220, 121, 221, 122, 222, 123, 124, 224 maylargely match vertical the distance, along the z-axis, between thebottom surface and the electrical terminals of the circulators 110, 210,111, 211, 112, 212, 113, 114, 214 or the termination resistors 120, 220,121, 221, 122, 222, 123, 124, 224. These may allow straightforwardsoldering or wire bonding after the circulators 110, 210, 111, 211, 112,212, 113, 114, 214 or the termination resistors 120, 220, 121, 221, 122,222, 123, 124, 224 are dropped into the sunken hole for mounting.

The configuration of the sites 311, 312, 313, 314 where the circulators110, 210, 111, 211, 112, 212, 113, 114, 214 are to be mounted are notlimited to these implementations. As far as electrical connections canbe made to the signal layer 240 via the solder pads, 231, 331 and anefficient thermal connection to the back plane layer 250 can be made viathe ground vias 251, any configuration of the sites 311, 312, 313, 314can be used.

FIG. 3b is a schematic that illustrates an exemplary integrated circuitboard for qubit readout circuit with references to FIGS. 1 and 2. Inparticular, FIG. 3b shows a mechanical drawing of the integrated circuitboard 300 when sunken holes are formed to mount the circulators 110,210, 111, 211, 112, 212, 113, 114, 214.

FIG. 3b shows that each of the sites 311, 312, 313, 314 is sunken suchthat part of a front plane layer 330 is lowered to form a thermalcontact area 332. As discussed above, most of the thermal contact area332 may not be visible from the top once the circulators 110, 210, 111,211, 112, 212, 113, 114, 214 are mounted. Also as discussed above, thethermal contact area 332 comprises a conducting layer which iselectrically and thermally connected to the back plane layer 350, notshown in FIG. 3b via the ground vias 251, also not shown in FIG. 3b .FIG. 3b also shows that each of the sites 311, 312, 313, 314 includes atthe level of the thermal contact area 332 a cylindrical void such thatthe all of the front plane layer 230, 330, the signal layer 240, theback plane layer 250 and the support layer 260, 360 are removed. Thephysical extent of such cylindrical voids may be determined such thatthe thermalization of the circulators 110, 210, 111, 211, 112, 212, 113,114, 214 are efficiently performed within the sites 311, 312, 313, 314.For example, in order to increase the thermal transfer, the area of thethermal contact area 332 may be increased and the extent of the voidsmay be decreased.

FIG. 3b shows that the first ports 111-1, 211-1, 112-1, 212-1, 113-1,114-1, 214-1, the second ports 111-2, 211-2, 112-2, 212-2, 113-2, 114-2,214-2 and the third ports 111-3, 211-3, 112-3, 212-3, 113-3, 114-3,214-3 of the circulators 111, 211, 112, 212, 113, 114, 214 areelectrically connected as described in FIGS. 1 and 3 a.

The lines in FIG. 3b representing the electrical connects may be at thelevel of the signal layer 240. In some implementations, the signal layer240 may comprise one or more stripline waveguides. As discussed above,in some implementations, the signal layer 240 and the thermal contactarea 332 may be at the same level within the integrated circuit board300. Also as discussed above, in some implementations, the signal layer240 may be at a higher level than the thermal contact area 332 to allowfor convenient electrical connection via soldering or wire bonding.

The design of the integrated circuit board 300 shown in FIG. 3b allowsfor independent clamping of circuit components on the integrated circuitboard 300 while enabling the circuit board 300 to act as a good thermalsink.

In some implementations, the integrated circuit board 300 may furtherinclude a magnetic shield tube 375, which is described later in FIG. 3c.

In some implementations, SMA connectors may be clamped to the inputterminal 301-1, the excite terminal 301-2, the output terminal 302, andthe pump terminal 303 of the integrated circuit board 300 such that asufficient amount of torque can be applied in fastening the SMAconnectors without damaging the board. The four holes around eachterminal 301-1, 301-2, 302, 303 are for mounting the SMA connectors withfour pins for alignment and grounding.

In some implementations, SMA connectors may be clamped to the input port301, output port 302, and the pump port 303 of the integrated circuitboard 300 such that a sufficient amount of torque can be applied infastening the SMA connectors without damaging the board. FIG. 3c is aschematic that illustrates a portion of an exemplary integrated circuitboard for a qubit readout circuit. In particular, FIG. 3c shows aschematic of the magnetic shield tube 375 and the configuration of theintegrated circuit board 300 around the site for the Josephson junctionparametric amplifier 370.

The circulators 110, 210, 111, 211, 112, 212, 113, 114, 214 may comprisemagnetized ferrite materials and the Josephson junction parametricamplifier 130 may be sensitive to the magnetic field since the operationof the Josephson junction is dependent on the magnetic flux bias appliedon it. Therefore, in order to integrate the circulators 110, 210, 111,211, 112, 212, 113, 114, 214 and the Josephson junction parametricamplifier 130 in a close proximity within one integrated circuit board300, the Josephson junction parametric amplifier 130 should be shieldedfrom the magnetic field generated by the circulators 110, 210, 111, 211,112, 212, 113, 114, 214 to a degree that it does not affect theoperation of the Josephson junction parametric amplifier 130.

FIG. 3c shows in the left panel the magnetic shield tube 375 when it isslotted in a slot 305 formed within the integrated circuit board. Thematerial for the magnetic shield tube 375 comprises a mu-metal, which isan alloy with a high magnetic permeability, often used for magneticshielding. The example of the material for the magnetic shield includesAmuneal 4K.

In some implementations, the magnetic shield tube 375 may be a separatecomponent from the integrated circuit board 300 and to be assembled byslotting into the slot 305 formed within the integrated circuit board300, as shown in the left panel of FIG. 3 c.

The magnetic shield tube 375 may comprise a mu metal shaped in the formof a cylinder with at least one of the faces open such that it can beslotted in to the slot 305 formed on at least one of the side surfacesof the integrated circuit board 300.

It is known that for effective magnetic shielding, the aspect ratio isone of the crucial parameters. In other words, the ratio between thelength of the magnetic shield tube 375 along the x-axis in FIG. 3c , andthe lateral extent of the cross section of the magnetic shield tube 375,along the y-axis in FIG. 3c determines the degree of magnetic shielding.Therefore, if the thickness of the integrated circuit board 300, alongthe z-axis in FIG. 3c , is kept small, the volume occupied by themagnetic shield tube 375 can be correspondingly small while maintainingthe aspect ratio of the magnetic shield tube 375. Since the thickness ofthe integrated circuit board 300 in the z-direction, may be determinedby the depth of the sunken holes to mount the circulators 110, 210, 111,211, 112, 212, 113, 114, 214 or the termination resistors 120, 220, 121,221, 122, 222, 123, 124, 224, if the extent of the circulators 110, 210,111, 211, 112, 212, 113, 114, 214 or the termination resistors 120, 220,121, 221, 122, 222, 123, 124, 224 in the z-direction, is kept small tokeep a low-profile, the volume of the magnetic shield tube 375 can bedecreased.

In some implementations, the slot 305 may be formed from one of thesides, for example in the y-z plane of FIG. 3c , of the integratedcircuit board 300 near the site for the Josephson junction parametricamplifier 370. The slot 305 includes at least two elongated channelswithin which the walls of the cylinder formed by the magnetic shieldtube 375 fit in.

In some implementations, the slot 305 may further include a recessionalong the side of the integrated circuit board in which the blocked endof the cylinder formed by the magnetic shield tube 375 is disposed suchthat it is flush with the side surface of the integrated circuit board300.

The right panel of FIG. 3c shows the cross section of the assembly ofthe integrated circuit board 300 and the magnetic shield tube 375 alongthe dotted line in the left panel of FIG. 3 c.

In some implementation, the extent of the interior of the cylinderformed by the magnetic shield tube 375, along the z-axis in FIG. 3c ,may be arranged to fit or to be larger than the thickness of theintegrated circuit board 300. In this case, the magnetic shield tube 375encloses, on one edge of the integrated circuit board 300 around thesite for the Josephson parametric amplifier 370, the front plane layer330, the signal layer 340, and the back plane layer 350 around the sitefor the Josephson parametric amplifier 370.

Alternatively, in some implementations, the slots 305 may be furtherformed such that the magnetic shield tube 375 encloses only the signallayer 340 and the site for the Josephson parametric amplifier 370, orsuch that the magnetic shield tube 375 encloses only the front planelayer 330, the signal layer 340 and the site for the Josephsonparametric amplifier 370, or such that the magnetic shield tube 375encloses only the signal layer 340, the site for the Josephsonparametric amplifier 370 and the back plane layer 370. As long as theaspect ratio of the magnetic shield tube 375 is maintained at a levelwhere the necessary magnetic shielding is obtained, the slot 305 aroundthe site for the Josephson parametric amplifier 370 may be arrangedaccordingly.

Compared to the case where magnetic shielding is achieved by the casingsof the circulators 110, 210, 111, 211, 112, 212, 113, 114, 214comprising a mu-metal, the implementations described above and shown inFIGS. 3b and 3c are more compact and also more effective forthermalization because only the site for the Josephson parametricamplifier 370 is magnetically shielded and because the material for thecasings of the circulators 110, 210, 111, 211, 112, 212, 113, 114, 214can be chosen to optimize thermalization rather than requiring magneticshielding. As such, the circulators 110, 210, 111, 211, 112, 212, 113,114, 214 can be disposed close to the Josephson parametric amplifier370, providing a more compact design of the integrated circuit board300. Furthermore, the tube-shape of the magnetic shield tube 375 and thefact that it is a separate component from the integrated circuit board300 provide more freedom in routing the electrical connections into andout of the site for the Josephson parametric amplifier 370 compared tothe case where the magnetic shielding is built into the integratedcircuit board 300.

FIG. 4 is a schematic that illustrates an exemplary qubit readoutassembly with references to FIGS. 1 to 3.

The qubit readout assembly 400 includes an expansion board 410. Theexpansion board 410 is configured to receive one or more the integratedcircuit boards or cards 200, 300 described above in FIGS. 2 and 3 in astacked configuration. The integrated circuit boards 200, 300 mayfurther include the circulators 110, 210, 111, 211, 112, 212, 113, 114,214 or the termination resistors 120, 220, 121, 221, 122, 222, 123, 124,224 mounted on the integrated circuit boards 200, 300 such that each ofthe integrated circuit boards 200, 300 form a qubit readout circuit 100described above in FIG. 1.

Each of the integrated circuit boards 200, 300 configured to form thequbit readout circuit 100 may serve as a pre-amplifying stage for asingle channel which includes a plurality of qubits coupled to a singlereadout transmission line via respective readout resonators. In case aplurality of channels of qubits are used for computation, acorresponding number of the integrated circuit boards 200, 300configured to form the qubit readout circuit 100 may be used.

Since each of the integrated circuit boards 200, 300 configured to formthe qubit readout circuit 100 is provided in a shape of a planar boardwith low-profile components mounted on it, the expansion board mayfurther comprise a plurality of sockets 411 arranged to receive theplurality of the integrated circuit boards 200, 300 configured to formthe qubit readout circuit 100 such that they are mounted on theexpansion board 410 largely parallel to one another. In particular, theplurality of sockets 411 may be formed such that the front plane layer230, 330 and the back plane layer 250, 350 are with a large surfacecontact with the body of the expansion board 410.

The expansion board 410 further includes a connector 412 which allowsconnection of the expansion board 410 with a cold finger 10 of thecryostat with a large surface contact. In case the cryostat is adilution refrigerator, the cold finger 10 may be the mixing plate of thedilution refrigerator which provides around 10 mK temperature.

It is crucial that the plurality of sockets 411 and the connector 412are arranged to allow an efficient thermal transfer between two partsjoined by the plurality of sockets 411 and the connector 412.

The expansion board 410 may comprise a material with a good thermalconductivity at a cryogenic temperature, such as copper. The expansionboard 410 may have a large enough volume and correspondingly a largeenough thermal capacity such that the temperature does not rise locallyat a certain position within the expansion board due to the heatreceived via the plurality of sockets 411 and such that the heatreceived is transferred to the cold finger 10 of the cryostatefficiently.

The shape and the types of the plurality of sockets 411 and theconnector 412 may be determined such that when the dilution refrigeratoris in operation and the temperature of the cold finger 10 is at its basetemperature, the plurality of the integrated circuit boards 200, 300attached to the expansion board 410 are at a thermal equilibrium withthe cold finger 10 and at a temperature largely equal to the temperatureof the cold finger 10.

In some implementations, the expansion board 410 may include electricalconnections connected to the input port 301, the output port 302, andthe pump port 303 of each of the integrated circuit boards 200, 300configured to form the qubit readout circuit 100. For example, a qubitchip containing the plurality of channels of qubits may be mounted onthe cold finger 10, which is the mixing plate of the dilutionrefrigerator and a HEMT (High Electron Mobility Transistor) amplifiermay be mounted on a 3K stage of the dilution refrigerator. The expansionboard 410 may be arranged such that it contains or mechanically supportsthe electrical connections from the qubit chip to the input port 301 andthe electrical connections from the output port 302 to the HEMTamplifier.

In some implementations, the expansion board 410 may form a tower mountto which the integrated circuit boards 200, 300 are mounted. Theexpansion board 410 and the integrated circuit boards 200, 300 mayprovide a highly modular system such that broken electrical lines can beeasily repaired and the circuit components mounted on the integratedcircuit boards can be replaced and/or reconfigured.

Using the design of the integrated circuit boards 200, 300 shown inFIGS. 2 and 3 and the expansion board shown in FIG. 4, the readout linesmay be constructed at a fraction of the size of an existing readoutline. For example, 30 readout lines may fit within the experimentalspace near the mixing plate of a dilution refrigerator.

Implementations of the quantum subject matter and quantum operationsdescribed in this specification can be implemented in suitable quantumcircuitry or, more generally, quantum computational systems, alsoreferred to as quantum information processing systems, including thestructures disclosed in this specification and their structuralequivalents, or in combinations of one or more of them. The terms“quantum computational systems” and “quantum information processingsystems” may include, but are not limited to, quantum computers, quantumcryptography systems, topological quantum computers, or quantumsimulators.

The terms “quantum information” and “quantum data” refer to informationor data that is carried by, held or stored in quantum systems, where thesmallest non-trivial system is a qubit, e.g., a system that defines theunit of quantum information. It is understood that the term “qubit”encompasses all quantum systems that may be suitably approximated as atwo-level system in the corresponding context. Such quantum systems mayinclude multi-level systems, e.g., with two or more levels. By way ofexample, such systems can include atoms, electrons, photons, ions orsuperconducting qubits. In some implementations the computational basisstates are identified with the ground and first excited states, howeverit is understood that other setups where the computational states areidentified with higher level excited states are possible. It isunderstood that quantum memories are devices that can store quantum datafor a long time with high fidelity and efficiency, e.g., light-matterinterfaces where light is used for transmission and matter for storingand preserving the quantum features of quantum data such assuperposition or quantum coherence.

Quantum circuit elements (also referred to as quantum computing circuitelements) include circuit elements for performing quantum processingoperations. That is, the quantum circuit elements are configured to makeuse of quantum-mechanical phenomena, such as superposition andentanglement, to perform operations on data in a non-deterministicmanner. Certain quantum circuit elements, such as qubits, can beconfigured to represent and operate on information in more than onestate simultaneously. Examples of superconducting quantum circuitelements include circuit elements such as quantum LC oscillators, qubits(e.g., flux qubits, phase qubits, or charge qubits), and superconductingquantum interference devices (SQUIDs) (e.g., RF-SQUID or DC-SQUID),among others.

In contrast, classical circuit elements generally process data in adeterministic manner. Classical circuit elements can be configured tocollectively carry out instructions of a computer program by performingbasic arithmetical, logical, and/or input/output operations on data, inwhich the data is represented in analog or digital form. In someimplementations, classical circuit elements can be used to transmit datato and/or receive data from the quantum circuit elements throughelectrical or electromagnetic connections. Examples of classical circuitelements include circuit elements based on CMOS circuitry, rapid singleflux quantum (RSFQ) devices, reciprocal quantum logic (RQL) devices andERSFQ devices, which are an energy-efficient version of RSFQ that doesnot use bias resistors.

Fabrication of the quantum circuit elements and classical circuitelements described herein can entail the deposition of one or morematerials, such as superconductors, dielectrics and/or metals. Dependingon the selected material, these materials can be deposited usingdeposition processes such as chemical vapor deposition, physical vapordeposition (e.g., evaporation or sputtering), or epitaxial techniques,among other deposition processes. Processes for fabricating circuitelements described herein can entail the removal of one or morematerials from a device during fabrication. Depending on the material tobe removed, the removal process can include, e.g., wet etchingtechniques, dry etching techniques, or lift-off processes. The materialsforming the circuit elements described herein can be patterned usingknown lithographic techniques (e.g., photolithography or e-beamlithography).

During operation of a quantum computational system that usessuperconducting quantum circuit elements and/or superconductingclassical circuit elements, such as the circuit elements describedherein, the superconducting circuit elements are cooled down within acryostat to temperatures that allow a superconductor material to exhibitsuperconducting properties. A superconductor (alternativelysuperconducting) material can be understood as material that exhibitssuperconducting properties at or below a superconducting criticaltemperature. Examples of superconducting material include aluminum(superconductive critical temperature of about 1.2 kelvin), indium(superconducting critical temperature of about 3.4 kelvin), NbTi(superconducting critical temperature of about 10 kelvin) and niobium(superconducting critical temperature of about 9.3 kelvin). Accordingly,superconducting structures, such as superconducting traces andsuperconducting ground planes, are formed from material that exhibitssuperconducting properties at or below a superconducting criticaltemperature.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of what may beclaimed, but rather as descriptions of features that may be specific toparticular implementations. Certain features that are described in thisspecification in the context of separate implementations can also beimplemented in combination in a single implementation. Conversely,various features that are described in the context of a singleimplementation can also be implemented in multiple implementationsseparately or in any suitable sub-combination. Moreover, althoughfeatures may be described above as acting in certain combinations andeven initially claimed as such, one or more features from a claimedcombination can in some cases be excised from the combination, and theclaimed combination may be directed to a sub-combination or variation ofa sub-combination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. For example, the actions recited in the claims can be performedin a different order and still achieve desirable results. In certaincircumstances, multitasking and parallel processing may be advantageous.Moreover, the separation of various components in the implementationsdescribed above should not be understood as requiring such separation inall implementations.

A number of embodiments have been described. Nevertheless, it will beunderstood that various modifications may be made without departing fromthe spirit and scope of the invention. Accordingly, other embodimentsare within the scope of the following claims.

The invention claimed is:
 1. An integrated qubit readout circuitcomprising: a superconducting parametric amplifier; a circuit boardarranged to mount the superconducting parametric amplifier; and acirculator mounted on the circuit board and connected to thesuperconducting parametric amplifier, wherein the circulator comprises atermination port electrically connected to a termination resistorarranged to terminate a pump tone received by the superconductingparametric amplifier, and wherein the termination resistor is mounted onthe circuit board.
 2. An integrated qubit readout circuit of claim 1,wherein at least part of an external surface of the termination resistoris in direct contact with the circuit board.
 3. An integrated qubitreadout circuit of claim 1, wherein at least part of an external surfaceof the circulator is in direct contact with the circuit board.
 4. Anintegrated qubit readout circuit of claim 3, wherein the circuit boardcomprises a front plane layer, a signal layer, a back plane layer, and asupport layer, wherein the front plane layer is disposed on a first sideof the support layer and the back plane layer is disposed on a secondside of the support layer that is opposite to the first side, whereinthe signal layer is disposed between the front plane layer and the backplane layer within the support layer, and wherein the circulator and thetermination resistor are mounted on the first side of the support layersuch that at least one surface of the circulator and the terminationresistor is in direct contact with the front plane layer.
 5. Anintegrated qubit readout circuit of claim 4, wherein the superconductingparametric amplifier is mounted on the signal layer.
 6. An integratedreadout circuit of claim 5, wherein the front plane layer, the signallayer and the back plane layer comprise a conductor whose thermalconductivity is larger than 300 W/m/K at 10 mK temperature, and whereinthe circulator and the termination resistor are mounted on the frontplane layer.
 7. An integrated qubit readout circuit of claim 6, whereinthe support layer comprises a first via arranged to electrically andthermally connect a first part of the front plane layer in contact withthe at least part of an external surface of the circulator to the backplane layer, and wherein the support layer comprises a second viaarranged to electrically connect a second part of the front plane layerto the signal layer.
 8. An integrated qubit readout circuit of claim 6,wherein the front plane layer comprises aluminum and the back planelayer comprises copper.
 9. An integrated qubit readout circuit of claim5, wherein the signal layer comprises a strip line waveguide.
 10. Anintegrated qubit readout circuit of claim 9, wherein the signal layercomprises a directional coupler formed with the strip line waveguide.11. An integrated qubit readout circuit of claim 4, wherein the backplane layer is connectable to a heat sink.
 12. An integrated qubitreadout circuit of claim 3, wherein the at least part of the externalsurface of the circulator in direct contact with the circuit boardcomprises a material whose thermal conductivity is larger than 300 W/m/Kat 10 mK temperature.
 13. An integrated qubit readout circuit of claim12, further comprising: a magnetic shield disposed around thesuperconducting parametric amplifier, arranged to shield thesuperconducting parametric amplifier from magnetic fields of thecirculator.
 14. An integrated qubit readout circuit of claim 13, whereinthe magnetic shield comprises a tube-shaped body comprising a mu-metalarranged to enclose the superconducting parametric amplifier when themagnetic shield is mounted on the circuit board.
 15. An integrated qubitreadout circuit of claim 14, wherein the circuit board comprises a firstslot arranged on a first side of the superconducting parametricamplifier and a second slot arranged on a second side of thesuperconducting parametric amplifier, wherein the first slot and thesecond slot are dimensioned so as to receive the magnetic shield, andwherein a distance between the first slot and the second slot matches adiameter of the magnetic shield.
 16. An integrated qubit readout circuitof claim 1, wherein the circulator comprises a passive ferritecirculator.
 17. An integrated qubit readout circuit of claim 1, whereinthe termination resistor comprises a 50 Ohm resistor.
 18. A qubitreadout assembly comprising: an expansion board connectable to a coldfinger of a cryostat; a plurality of the integrated qubit readoutcircuits of claim 1, wherein the expansion board is configured toreceive the plurality of the integrated qubit readout circuits such thatthe plurality of the integrated qubit readout circuits are mounted onthe expansion board, wherein the expansion board is configured such thatthe expansion board and the plurality of the integrated qubit readoutcircuits are in a thermal equilibrium with the cold finger of thecryostat when the expansion board is connected to the cold finger andthe plurality of the integrated qubit readout circuits are mounted onthe expansion board, and wherein the expansion board is configured toprovide electrical connections between a circuit in contact with thecold finger and the plurality of the integrated qubit readout circuits.